Question: Simplify the following expression: $k = \dfrac{-5t^2 + 20t + 225}{t + 5} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ k =\dfrac{-5(t^2 - 4t - 45)}{t + 5} $ Then we factor the remaining polynomial: $t^2 {-4}t {-45} $ ${5} {-9} = {-4}$ ${5} \times {-9} = {-45}$ $ (t + {5}) (t {-9}) $ This gives us a factored expression: $\dfrac{-5(t + {5}) (t {-9})}{t + 5}$ We can divide the numerator and denominator by $(t - 5)$ on condition that $t \neq -5$ Therefore $k = -5(t - 9); t \neq -5$